Romantic Turn • You are driving with a “friend” who is sitting to your right on the passenger side of the front seat. You would like to be closer to your “friend” and decide to use your knowledge of physics to achieve your romantic goal. So you'll make a sharp turn. Which direction should you turn so as to make your friend slide closer to you? If the coefficient of static friction between your friend and the seat of the car is 0.40, and you drive at a constant speed of 18 m/s, what is the maximum radius you could make your turn and still have your friend slide your way?
Project • Sweep a bowling ball around a chair with a broom. • Which way do you sweep to keep the ball moving in a circle? • Why? • What does the bowling ball “want” to do?
5/8/07 Lesson #72Topic: Circular Motion Objectives: (After this class I will be able to) 1. Describe and explain centripetal acceleration and force. Warm Up: A merry-go-round has a radius of 6m and makes a full rotation every 5 seconds. What is the speed of a horse on the outer edge of the ride? Assignment: Concept Development 9-2
0 of 5 A merry-go-round has a radius of 6m and makes a full rotation every 5 seconds. What is the speed of a horse on the outer edge of the ride? • 1.2m/s • 2.4m/s • 7.5m/s • 30m/s
Tangential Velocity • A horse on a merry-go-round has velocity tangent to the circle. • Its velocity is always perpendicular to the radius of the circle. r v
Rotate vs. Revolve • Rotation: An object spinning around a point located within the object. • Example: The Earth rotates about its axis. • Revolution: An object moving in a circle around a point in space. • Example: The Earth revolves around the Sun.
Centripetal Force • An object in motion will stay in motion in a straight line unless acted on by an outside force. • This means that a force must be acting on an object that is moving in a circle. • The force causing an object to move in a circle is called the Centripetal Force. • Centripetal = center seeking. • demo
Centripetal Acceleration • Acceleration = an object speeding up, slowing down, or changing direction. • An object moving in a circle is constantly changing direction. • Centripetal force causes the object to accelerate towards the center of the circle. • The tangential velocity prevents the object from going straight towards the center. • Example: Moon around Earth
Centripetal Acceleration Equation a = centripetal acceleration v = tangential velocity r = radius Centripetal Force Equation
0 of 5 A runner moving at a speed of 8.8m/s rounds a bend with a radius of 25m. What is the centripetal acceleration of the runner? • 0.352m/s2 • 3.10m/s2 • 3.10m/s
An airplane traveling at 201 m/s makes a turn. What is the smallest radius of the circular path (in km) that the pilot can make and keep the centripetal acceleration under 5.0 m/s2? • 8080.2 km • 40.2 km • 8.08 km • 7820.6 km
A 45 kg merry-go-round worker stands on the ride’s platform 6.3 m from the center. If her speed as she goes around the circle is 4.1 m/s, what is the force of friction necessary to keep her from falling off the platform? • 29.29 N • 120.07 N • 29.29 m/s2 • 120.07 m/s2
A car racing on a flat track travels at 22 m/s around a curve with a 56 m radius. Find the car’s centripetal acceleration. What minimum coefficient of static friction between the tires and road is necessary for the car to round the curve without slipping? • 8.64 • 864.29 m/s2 • .86 N • .86
Project • List objects that move in circles. • List what is causing the centripetal force for each object. • Describe the “Romantic Turn” and what the maximum radius can be and yet still achieve your goal. (Would this trick ever actually work on anyone?)
4/30/07 Lesson #73Topic: Lab: Circular Motion Objectives: (After this class I will be able to) Solve for the tangential velocity of a whirling object. Calculate for the mass of a rubber stopper using the centripetal force equation. Lab Task: Find the mass of a rubber stopper using Fc=mv2/r Assignment: Lab Report due tomorrow (show all calculations!)
Croc Dundee Noisemaker • After watching the movie "Crocodile Dundee," you and some friends decide to make a communications device invented by the Australian Aborigines. It consists of a noise-maker swung in a vertical circle on the end of a string. Your design calls for a 400 gram noise-maker on a 60 cm string. You are worried about whether the string you have will be strong enough, so you decide to calculate the tension in the string when the device is swung with an acceleration which has a constant magnitude of 20 m/s2 . You and your friends can't agree whether the maximum tension will occur when the noise maker is at the highest point in the circle, at the lowest point in the circle, or is always the same. To settle the argument you decide to calculate the tension at the highest point and at the lowest point and compare them.
Project • Loop the loop track • Describe what makes the ball make it around the loop. • Draw the forces acting on the ball at the top of the loop and at the bottom of the loop.
4/31/07 Lesson #74Topic: Non-Uniform Circular Motion Objectives: (After this class I will be able to) 1. Describe inertial and non-inertial reference frames. 2. Define Centrifugal Force. 3. Solve problems involving Non-Uniform circular motion. Warm Up: A 615kg racecar completes one lap in 14.3s around a circular track with a radius of 50m. The car moves at constant speed. What is the acceleration of the car? Assignment: Non- Uniform Circular motion
0 of 5 A 615kg racecar completes one lap in 14.3s around a circular track with a radius of 50m. The car moves at constant speed. What is the acceleration of the car? • 9.65m/s2 • 0.44m/s2 • 0.24m/s2 • 0 m/s2
Inertial Reference Frame • Inertial Reference Frame = explanations of observations where Newton’s laws hold true. • Example: Watching a car race on a circular track. Friction is the centripetal force accelerating the cars towards the center of the track.
Non-Inertial Reference Frame • Non-Inertial Reference Frame = an imaginary force needs to exist for Newton’s laws to hold true. • Example: Being in a car going around a circular race track. You feel pushed towards one side of the car. • You can say that this “push” is some imaginary force rather than the inertia of your body. • This imaginary force is called the centrifugal force. • Centrifugal = center fleeing
Non-Uniform Circular Motion • The motion of an object is non-uniform when other forces are acting on it besides the centripetal force. • Example: An object moving in a vertical circle.
B r =10m A Non-Uniform Circular Motion Problems • When solving non-uniform problems, Fnet = 0 and use centrifugal force instead of centripetal force. • Example: A roller coaster car speeds down a hill past point A and then rolls up a hill past point B • a. The car has a speed of 20m/s at point A. If the normal force is 20600N at this point, what is the mass of the car?
B A Non-Uniform Circular Motion Problems • Example: A roller coaster car speeds down a hill past point A and then rolls up a hill past point B • b. What is the maximum speed the car can have at point B for the gravitational force to hold it on the track? r = 15m
0 of 5 A carnival clown rides a motorcycle down a ramp and around a vertical loop. If the loop has a radius of 18m, what is the slowest speed the rider can have at the top of the loop to avoid falling? • 4.24m/s • 13.4m/s • 18m/s • 180m/s
0 of 5 A 1.13kg ball is swung vertically from a 0.5m cord in circular motion at a speed of 2.4m/s. What is the tension in the cord at the bottom of the ball’s motion? • 11.3N • 13.0N • 24.3N • 1.7N
0 of 5 A mythical warrior swings a 5.6kg mace on the end of a magically massless 86cm chain in a horizontal circle above his head. The mace makes one full revolution in 1.8s. Find the tension in the magical chain. • 1.49N • 58.7N • 5868N • 28.0N
Croc Dundee Noisemaker • Find the tension in the noisemaker at both top and bottom of the vertical circle.
Bonus • A passenger train traveling at constant speed rounds a curve of radius 275m. A chandelier suspended from the ceiling swings out to an angle of 17.5° throughout the turn. What is the speed of the train?